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In this letter, we investigate the outage-constrained robust secure design in a multiple-input single-output (MISO) energy harvesting (EH) cognitive radio network (CRN), where the malicious energy receivers (ERs) may wiretap the desired information and hence can be treated as potential eavesdroppers (Eves). In particular, considering a non-linear energy harvesting (EH) model, our objective is to design the transmit covariance matrix to maximize the secrecy energy efficiency (SEE) under the given outage probability and transmit power constraints, while satisfying the EH and quality-of-service (QoS) requirements. To tackle the original non-convex problem, we resort to semidefinite relaxation (SDR) and Bernstein-type inequality (BTI)based approximations to reformulate it into a tractable form. Then, the original problem becomes decomposable and can be efficiently solved by handling a two-stage optimization problem. At last, numerical results are provided to demonstrate the effectiveness and superior performance of the proposed design in comparisons with the existing schemes. Index Terms-Cognitive radio network (CRN), energy harvesting, secrecy energy efficiency (SEE), outage probability.

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